Scheduling the charging periods for a large set of electric vehicles with the objective of satisfying the user demands may be a very hard problem due to the physical constraints of the charging stations. In this paper, we consider a problem of this family which is motivated by a real life situation where a set of users demand electric charge while their vehicles are parked. Each stall has a charging point which is connected to one of the lines of a three-phase electric feeder. There are power constraints that limit the number of vehicles that can be charging at the same time on the same line and balance constraints that limit the difference in the number of vehicles charging in every two lines. We model this problem in the framework of Dynamic Constraint Satisfaction Problem (DCSP) with Optimization, and propose a solution procedure that requires solving a sequence of CSPs over time. Each one of these CSPs requires in its turn solving three instances of a one machine sequencing problem with variable capacity. This procedure was implemented on a simulator of the charging station and evaluated on a number of instances defined from different scenarios of vehicle arrivals and energy requirements. The results of the experimental study show clearly that the proposed algorithm is effective and that it produces schedules much better than those computed by a classic dispatching rule.

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This paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its components but it is also quite competitive with the state-of-the-art when solving both crisp and fuzzy instances, providing new best-known solutions for a number of these test instances. Genetic Tabu AbstractThis paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its component...

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Rodríguez Molins, M.; Ingolotti Hetter, LP.; Barber Sanchís, F.; Salido Gregorio, MA.; R. Sierra, M.; Puente, J. (2014). A genetic algorithm for robust berth allocation and quay crane assignment. Progress in Artificial Intelligence. 2(4): 177-192. doi:10.1007/s13748-014-0056-3. A Genetic Algorithm for Robust Berth Allocation and Quay Crane AssignmentAbstract Scheduling problems usually obtain the optimal solutions assuming that the environment is deterministic. However, actually the environment is dynamic and uncertain. Thus, the initial data could change and the initial schedule obtained might be unfeasible. To overcome this issue, a proactive approach is presented for scheduling problems without any previous knowledge about the incidences that can occur. In this paper, we consider the Berth Allocation Problem and the Quay Crane Assignment Problem as a representative example of scheduling problems where a typical objective is to minimize the service time. The robustness is introduced within this problem by means of buffer times that should be maximized in order to absorb possible incidences or breakdowns. Therefore, this problem becomes a multi-objective optimization problem with two opposite objectives: minimizing the total service time and maximizing the robustness or buffer times.